In this paper, we establish the existence theorems of simultaneous equilibriums. As consequence of our results, we establish the existence theorem of simultaneous mathematical program and equilibrium problem and existence theorems of generalized vector quasi-saddle point problems .

The network equations of electric power system are formed in which the node voltages and branch currents are as state variables by π equivalent circuit simulation of power components. The explicit expressions of power system voltage equilibrium solution curves are obtained by solving the equations above, and then get the characteristic equation of the saddle-node bifurcation point, define the f...

In this paper we proposed a modified Lagrangian functional for obstacle problem, investigated its properties. Then we construct Uzawa method for finding a saddle point, proved the convergence theorems. Some numerical examples are provided.

We establish the saddle point property of the focusing selfsimilar solution of a free boundary problem for the heat equation with free boundary conditions given by u = 0 and ∂u ∂ν = 1.

We propose a new gradient based scheme to approximate Nash equilibria of large sequential two-player, zero-sum games. The algorithm uses modern smoothing techniques for saddle-point problems tailored specifically for the polytopes used in the Nash equilibrium problem.

The paper provides two contributions. First, we present new convergence results for conditional e-subgradient algorithms for general convex programs. The results obtained here extend the classical ones by Polyak [Sov. Math. Doklady 8 (1967) 593; USSR Comput. Math. Math. Phys. 9 (1969) 14; Introduction to Optimization, Optimization Software, New York, 1987] as well as the recent ones in [Math. P...

We establish existence and multiplicity theorems for a Dirichlet boundary-value problem at resonance. This problem is a nonlinear subcritical perturbation of a linear eigenvalue problem studied by Cuesta, and includes a sign-changing potential. We obtain solutions using the Mountain Pass lemma and the Saddle Point theorem. Our paper extends some recent results of Gonçalves, Miyagaki, and Ma.

In this paper, we prove a nonlinear separation associated with a constrained multiobjective optimization problem in the image space, as well as the equivalence between the existence of nonlinear separation function and a saddle point condition for a generalized Lagrangian function associated with the given problem. As applications, we obtain some equivalent conditions on exact penalty methods f...

In this paper, a Signorini problem is reduced to a variational inequality on the boundary, and a direct boundary element method is presented for its solution. Furthermore, error estimates for the approximate solutions of Signorini problems are given. In addition, we show that the Signorini problem may be formulated as a saddle-point problem on the boundary.

In this paper, we further investigate the local Hermitian and skew-Hermitian splitting (LHSS) iteration method and the modified LHSS (MLHSS) iteration method for solving generalized nonsymmetric saddle point problems with nonzero (2,2) blocks. When A is non-symmetric positive definite, the convergence conditions are obtained, which generalize some results of Jiang and Cao [M.-Q. Jiang and Y. Ca...